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Baby Circle

A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?

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Orthogonal Circle

Given any three non intersecting circles in the plane find another circle or straight line which cuts all three circles orthogonally.

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Ellipses

Here is a pattern for you to experiment with using graph drawing software. Find the equations of the graphs in the pattern.

Square Pair Circles

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

For example

25 = 02 + (±5)2 = (±5)2 + 02 = (±3)2 + (±4)2 = (±4)2 + (±3)2

and this shows that there are 12 points with integer coordinates on the circle x2+ y2 = 52 with centre at the origin and radius 5 units.